A Quantum-Inspired Algorithm for the Factorized Form of Unitary Coupled Cluster Theory

TL;DR

This paper introduces a quantum-inspired classical algorithm for the factorized form of unitary coupled cluster theory, enhancing the understanding and testing of UCC as a wave-function ansatz for quantum and classical computations.

Contribution

It presents an exact operator identity-based classical algorithm for UCC, facilitating benchmarking and insights into its effectiveness for strongly correlated systems.

Findings

UCC shows potential for strongly correlated systems where conventional methods struggle.

The classical algorithm enables extensive testing and benchmarking of UCC techniques.

UCC can serve as an effective initial state for quantum phase estimation, improving ground state overlap.

Abstract

The factorized form of unitary coupled cluster theory (UCC) is a promising wave-function ansatz for the variational quantum eigensolver algorithm. Here, we present a quantum inspired algorithm for UCC based on an exact operator identity for the individual UCC factors. We implement this algorithm for calculations of the H$_{10}$ linear chain and the H$_2$O molecule with single and double $\zeta$ basis sets to provide insights about UCC as a wave-function ansatz. We find that as an electronic structure method, UCC could potentially be valuable for strongly correlated systems, for which conventional coupled cluster theory has difficulties. On quantum computers, the factorized form of UCC can also serve as an initial state preparation method for the quantum phase-estimation algorithm, since it yields higher overlap with the ground state than many other common variational ansatzes. This classical algorithm for UCC also enables widespread testing of the technique, which will be useful for benchmarking quantum computations.